MinT - Best Known (104−87, 104, s)-Nets in Base 27

Best Known (104−87, 104, s)-Nets in Base 27

(104−87, 104, 96)-Net over F₂₇ — Constructive and digital

Digital (17, 104, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 104, 96)-net over F₂₇, using
- net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
    - an explicitly constructive algebraic function field [i]

(104−87, 104, 144)-Net over F₂₇ — Digital

Digital (17, 104, 144)-net over F₂₇, using

t-expansion [i] based on digital (16, 104, 144)-net over F₂₇, using
- net from sequence [i] based on digital (16, 143)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 16 and N(F) ≥ 144, using
    - a curve from the manYPoints database [i]

(104−87, 104, 1719)-Net in Base 27 — Upper bound on s

There is no (17, 104, 1720)-net in base 27, because

1 times m-reduction [i] would yield (17, 103, 1720)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 2717 017084 894472 624867 369363 311271 681798 462204 024209 915523 166237 336272 542814 883931 980418 104969 965442 355570 321416 890035 011122 455804 352784 818612 940705 > 27¹⁰³ [i]